# How do you find a fraction between 1/2 and 4/5?

Apr 13, 2017

There are many more than one fraction in the middle

#### Explanation:

There are an infinite number of fractions in between $\frac{1}{2}$ and $\frac{4}{5}$. We'll find first the middle point between these two, and then we'll show that you can find as many as you like in between $\frac{1}{2}$ and $\frac{4}{5}$.

The middle point between $a$ and $b$ is $\frac{a + b}{2}$.

So the middle point between $\frac{1}{2}$ and $\frac{4}{5}$ is $\frac{\frac{1}{2} + \frac{4}{5}}{2} = \frac{\frac{5 + 8}{10}}{2} = \frac{13}{20}$

But you can do the same now and find the middle point between $\frac{1}{2}$ and $\frac{13}{20}$, and also the middle point between $\frac{13}{20}$ and $\frac{4}{5}$, and so on. You can find as many points as you want between $\frac{1}{2}$ and $\frac{4}{5}$

Apr 13, 2017

There are infinitely many - change to a common denominator for comparison.

#### Explanation:

Before you can do any comparison between fractions, change them to the same denominator.

1/2 < ? < 4/5

There are infinitely many fractions between these two fractions.

5/10 < color(blue)(?) < 8/10

Now we can see that a fraction between these can be
$\textcolor{b l u e}{\frac{6}{10} \text{ or } \frac{7}{10}}$

However, you can use any common denominator, not only the lowest.

For example:" "15/30 < color(red)(?) < 24/30

You could use $\textcolor{red}{\frac{16}{30} , \text{ "17/30," "18/30," "18/30," "19/30," "20/30," "21/30," "22/30," } \frac{23}{30}}$

And so on .....

The fraction exactly halfway would be: $\frac{\frac{6 + 7}{2}}{10} = \frac{6.5}{10} = \frac{13}{20}$